Hydrostatic Bearing Systems
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Transcript of Hydrostatic Bearing Systems
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Hydrostatic Bearing Systems
Figure 13.1 Formation of fluid in hydrostatic bearing system. (a) Pump off; (b) pressure build up; (c) pressure times recess area equals normal applied load; (d) bearing operating; (e) increased load; (f) decreased load. [From Rippel (1963)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Circular Step Pad & Pressure
Figure 13.2 Radial-flow hydrostatic thrust bearing with circular step pad.
Figure 13.3 Pressure distribution in radial-flow hydrostatic thrust bearing.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pad Coefficients
Figure 13.4 Chart for determining bearing pad coefficients for circular step thrust bearing. [From Rippel (1963)].
Load coefficient:
Flow coefficient:
Power coefficient:
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Annular Thrust Pad Bearing
Figure 13.5 Configurations of annular thrust pad bearing. [From Rippel (1963)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pad Coefficients
Figure 13.6 Chart for determining bearing pad coefficients for annular thrust pad bearings. [From Rippel (1963)].
Load coefficient:
Flow coefficient:
Power coefficient:
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Rectangular Hydrostatic Pad
Figure 13.7 Rectangular hydrostatic pad.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pad Coefficients
Figure 13.8 Pad coefficients. (a) Square pad; (b) rectangular pad with B= 2L and b = l.
Load coefficient:
Flow coefficient:
Power coefficient:
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Compensated Hydrostatic Bearings
Figure 13.9 Capillary-compensated hydrostatic bearing. [From Rippel (1963)].
Figure 13.10 Orifice-compensated hydrostatic bearing. [From Rippel (1963)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Flow-Valve Compensation
Figure 13.10 Constant-flow-valve compensation in hydrostatic bearing. [From Rippel (1963)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Compensating Element Ranking
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Speed vs. Load
Figure 14.1 Effect of speed on load for self-acting, gas-lubricated bearings. [From Ausman (1961).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Rectangular-Step Thrust Bearing
Figure 14.2 Rectangular-step thrust bearing. [From Hamrock (1972).]
Figure 14.3 Transformation of rectangular slider bearing into circular sector bearing.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Optimum Step
Parameters
Figure 14.4 Effect of dimensionless bearing number on optimum step
parameters. (a) For maximum dimensionless load-carrying capacity; (b)
for maximum dimensionless stiffness. [From Hamrock (1972).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Load-Carrying
Capacity & Stiffness
Figure 14.5 Effect of dimensionless bearing number on dimensionless load-
carrying capacity and dimensionless stiffness. (a) For maximum
dimensionless load-carrying capacity; (b) for maximum dimensionless stiffness.
[From Hamrock (1972).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Spiral-Groove Thrust Bearing
Figure 14.6 Spiral-groove thrust bearing. [From Malanoski and Pan (1965).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Spiral-Groove Thrust
Bearing Characteristic
s
Figure 14.7 Charts for determining characteristics of spiral-groove thrust
bearings. (a) Groove factor; (b) load; (c) stiffness; (d) torque; (e) flow; (f) optimal
groove geometry; (g) groove length factor. [From Reiger (1967).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure Perturbation Solution
Figure 15.1 Design chart for radially loaded, self-acting, gas-lubricated journal bearings (isothermal first-order perturbation solution.) [From Ausman (1959).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Linearized ph Solution
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Pivoted-Pad Bearings
Figure 15.3 Geometry of individual pivoted-pad bearing. [From Gunter et al. (1964)]
Figure 15.4 Geometry of pivoted-pad journal bearing with three pads. [From Gunter et al. (1964)]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pivoted-Pad Perfor-mance Parameters
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Herringbone-Groove Journal Bearing
Figure 15.6 Configuration of concentric herringbone-groove journal bearing.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Parameters for Herringbone Bearing
Figure 15.7 Charts for determining optimal herringbone-journal-bearing groove parameters for maximum radial load. Top plots are for grooved member rotating; bottom plots are for smooth member rotating. (a) Optimal film thickness ratio; (b) optimal groove width ratio. [From Hamrock and Fleming (1971)]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Parameters for Herringbone Bearing
(cont.)
Figure 15.7 Concluded. (c) Optimal groove length ratio; (d) optimal groove
angle.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Load-Carrying Capacity
Figure 15.8 Chart for determining maximum normal load-carrying capacity. (a) grooved member rotating; (b) smooth
member rotating. [From Hamrock and Fleming (1971)]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Stability of Herringbone-Groove Bearings
Figure 15.9 Chart for determining maximum stability of herringbone-groove
bearings. [From Fleming and Hamrock (1974).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Foil Bearing
Figure 15.10 (a) Schematic illustration of a foil bearing; (b) free-body diagram of a section of foil.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure in Foil Bearing
Figure 15.11 Pressure distribution and film thickness in a foil bearing. [From Bhushan (2002).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Lubrication of Rigid Cylinder
Figure 16.1 Lubrication of a rigid cylinder near a plane. (a) Coordinates and surface velocities; (b) forces.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Cavitation Fingers
Figure 16.2 Cavitation fingers.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Effect of Leakage
Figure 16.4 Effect of leakage on tangential load component.
Figure 16.3 Side-leakage effect on normal load component.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Contact Geometry
Figure 16.5 Contact geometry. (a) Two rigid solids separated by a lubricant film:
(a-1) y=0 plane; (a-2) x=0 plane. (b) Equivalent system of a rigid solid near a plane separated by a lubricant film: (b-1) y=0 plane; (b-2) x=0 plane. [From Brewe
et al. (1979)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Boundary Conditions & Nodal Structure
Figure 16.6 Effect of boundary conditions. (a) Solution using full Sommerfeld boundary conditions; (b) solution using half Sommerfeld boundary condition; (c) solution using Reynolds boundary conditions. [From Brewe et al. (1970)].
Figure 16.7 Variable nodal structure used for numerical calculations. [From Brewe et al. (1979)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Hydrodynamic Lift
Figure 16.8 Effect of radius ratio on reduced hydrodynamic lift. [From Brewe et al. (1979)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure for Two Radius
Ratios
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure Contours
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Comparison of Fully Flooded and Starved
Contact
Figure 16.11 Three-dimensional representation of
pressure distributions for dimensionless minimum film
thickness Hmin of 1.0 x 10-4. (a) Fully flooded condition;
(b) starved condition. [From Brewe and Hamrock. (1982)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Comparison of Fully Flooded and Starved
Contact
Figure 16.11 Three-dimensional representation of
pressure distributions for dimensionless minimum film
thickness Hmin of 1.0 x 10-3. (a) Fully flooded condition; (b)
starved condition. [From Brewe and Hamrock. (1982)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure Contours - Starved
Figure 16.13 Isobaric contour plots for three fluid inlet levels for dimensionless minimum film thickness Hmin of 1.0 x 10-4. (a) Fully flooded condition: dimensionless fluid inlet level Hin, 1.00; dimensionless pressure, where dP/dX=0, Pm, 1.20 x 106; dimensionless load-speed ratio W/U, 1153.6. (b) Starved condition; Hin, 0.004; Pm = 1.19 x 106; W/U = 862.6. (c) Starved condition: Hin =0.001; Pm = 1.13 x 106; W/U = 567.8. [From Brewe and Hamrock. (1982)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Inlet Level Effect
Figure 16.14 Effect of fluid inlet level on film thickness reduction factor in flooded conjunctions. [From Brewe and Hamrock (1982)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Lubricant Flow
Figure 16.15 Lubricant flow for a rolling-sliding contact and corresponding pressure buildup. [From Ghosh et al. (1985)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Effect of Velocity
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Pressure Distribution
s vs. Normal Velocity
Parameter
Figure 13.2 Radial-flow hydrostatic thrust bearing with circular step pad.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Performance Parameters
Figure 16.19 Effect of radius ratio on dynamic load ratio. Dimensionless central film thickness Hmin, 1.0 x 10-4; dimensionless fluid inlet level Hin, 0.035. [From Ghosh et al. (1985)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Peak Pressure vs. Radius Ratio
Figure 16.20 Effect of radius ratio on dynamic peak pressure ratio. Dimensionless central film thickness Hmin, 1.0 x 10-4; dimensionless fluid inlet level Hin, 0.035. [From Ghosh et al. (1985)].
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Contact Geometry
Figure 17.1 Geometry of contacting elastic solids. [From Hamrock and Dowson (1981).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Radii of Curvature
Figure 17.2 Sign designations for radii of curvature of various machine elements. (a) Rolling elements; (b) ball bearing races; (c) rolling bearing races.
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure Distribution
Figure 17.3 Pressure distribution in ellipsoidal contact.
Pressure:
Maximum pressure:
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Ellipticity Parameter and Elliptic Integrals
Figure 17.4 Variation of ellipticity parameter and elliptic integrals of first and second kinds as function of radius ratio. [From Hamrock and Brewe (1983).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Hertz Contact SummaryContact dimensions:
Maximum elastic deformation:
Effective elastic modulus:
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Elliptic Integrals
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Effect of Radius Ratio on Subsurface Stress
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Simplified Equations for Elliptic Integrals
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Conformity
Figure 17.5 Three degrees of conformity. (a) Wheel on rail; (b) ball on plane; (c) ball-outer-race contact. [From Hamrock and Brewe (1983).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Calculation of Elastic Deformation
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Load Components
Figure 18.1 Sketch to illustrate calculations of Xr,end and N. [From Houpert and Hamrock (1986).]
Figure 18.2 Load components and shear forces. [From Hamrock and Jacobson (1984).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Profiles at Early
Iterations
Figure 18.3 Pressure profiles and film shapes at iterations 0, 1, and 14 with
dimensionless speed, load, and material parameters fixed at U = 1.0 x 10-11, W’ =
2.045 x 10-5, and G=5007. [From Houpert and Hamrock (1986).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure and Film Profiles
Figure 18.4 Dimensionless pressure profiles for isoviscous and viscous solutions. Compressibility effects were considered. [From Hamrock et al. (1988).]
Figure 18.5 Film thickness profiles for isoviscous and viscous solutions. Compressibility effects were considered. [From Hamrock et al. (1988).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Detail of Spike Location
Figure 18.6 Pressure and film thickness profiles in region 0.9 ≤ Xr ≤ 1.0. (a) Dimensionless pressure; (b) dimensionless film thickness. [From Hamrock et al. (1988).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Compressibility Effect
Figure 18.8 Dimensionless pressure and film thickness profiles for an incompressible fluid. Viscous effects were considered. [From Hamrock et al. (1988).]
Figure 18.9 Dimensionless pressure and film thickness profiles for a compressible fluid. Viscous effects were considered. [From Hamrock et al. (1988).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Detail of Spike Location
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Pressure as a Function of Load
Figure 18.11 Variation of dimensionless pressure in elastohydrodynamically lubricated conjunction for six dimensionless loads with dimensionless speed and materials parameters held fixed at U=1.0 x 10-11 and G=5007. [From Pan and Hamrock (1989).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Speed Effects
Figure 18.12 Variation of dimensionless pressure in elastohydrodynamically
lubricated conjunction for three dimensionless speeds with
dimensionless load and materials parameters held fixed at W’ = 1.3 x 10-4 and G=5007. [From Pan and Hamrock
(1989).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Spike Amplitude
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Spike Location
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Film Thickness
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Variation in Film Shape
Figure 18.13 Variation of dimensionless film shape in
elastohydrodynamically lubricated conjunction for six dimensionless
loads with dimensionless speed and materials parameters held fixed at U=1.0 x 10-11 and G=5007. [From
Pan and Hamrock (1989).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Central Film Thickness
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Film Shape for Different Speeds
Figure 18.14 Variation of dimensionless film shape for three dimensionless
speeds with dimensionless load and materials parameters fixed at W’ = 1.3 x
10-4 and G=5007. [From Pan and Hamrock (1989).]
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Location of Minimum Film Thickness
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Center of Pressure
Fundamentals of Fluid Film LubricationHamrock, Schmid & JacobsonISBN No. 0-8247-5371-2
Mass Flow Rate